Over a wireless multiple-input-multiple-output (MIMO) multiple access channel (MAC), several users (mobiles) communicate simultaneously to a common receiver, known in cellular communications as the base-station. Uplink space-division multiple access (SDMA), where multiple users of the same sector/cell share the same set of resources at a given time, coupled with advanced receiver processing at the base-station can lead to a dramatic increase in system throughput. Traditionally, strictly orthogonal (non-SDMA) uplink systems such as TDMA/FDMA have been preferred since the simple, albeit sub-optimal, match filter receivers employed at base-stations so far are not suitable for SDMA. The advent of multiple receive antennas at the base-station, however, and improvements in technology have made possible the use of advanced receiver processing and hence SDMA. Consequently, quasi-orthogonal OFDMA and IFDMA, where subsets of users are allocated the same resources, are being proposed to accommodate ambitious future throughput requirements. A challenge is to design scheduling and receiver processing algorithms that garner most of the throughput increase promised by SDMA but with practically feasible complexities.
SDMA is also being considered to obtain throughput improvements in downlink systems where the transmitter (base-station) as well as each user have multiple antennas. Multi-stream MIMO schemes have been proposed, where over each resource block, the base-station transmits multiple independent streams to the intended user. Note that there is a direct analogy between independent single-antenna users in the SDMA uplink and the independent multiple streams in the downlink. The role of the base-station in the uplink is assumed by the intended multiple-receive-antenna user in the downlink. A challenge again is to obtain the throughput increase promised by SDMA with practically feasible complexities.
Other studies have looked into the scheduling (i.e. rate-assignment) problem for minimum mean square error (MMSE)-based successive interference cancellers (SIC). Although in theory, a MMSE-SIC decoder is (sum) capacity achieving for an SDMA configuration, in practice, a more advanced receiver such as an MMSE-based successive group decoder (SGD) may considerably increase throughput. In a practical system, the transmission rate for each user is chosen from a finite set of limited granularity, therefore, for each channel realization, the number of possible rates for a general successive group decoder is greater because its capacity region is larger than that of MMSE-SIC. As a result, a rate-assignment having a higher sum can be chosen and fed back to the users.
On a flat-fading MAC, due to stringent delay-constraints, each transmitted codeword experiences just one (or few) fading realization(s). Outage probability has emerged as a useful tool for such non-ergodic (slow-fading) settings. For a MAC where only the receiver has perfect channel state information (CSI), an outage can be declared simultaneously for all users if the rate vector containing the information rates of all (active) users lies outside the instantaneous achievable rate region, which in turn is a function of the instantaneous channel state and the decoder used. Occurrence of this outage event, henceforth referred to as the common outage, indicates that a joint error event (i.e., event that at least one user is decoded erroneously) is very likely and the common outage probability, denoted by Pr(), represents an achievable joint or frame error probability (FEP). Pr() was derived in D. N. C. Tse et al. “Diversity-multiplexing tradeoff in multiple-access channels,” IEEE Trans. Inform. Theory, vol. 50, no. 9, pp. 1859-1874, September 2004 for the case where the receiver employs the optimum joint decoder, and in N. Prasad et al., “Outage based analysis for MultiaccessNV-BLAST architecture over MIMO block Rayleigh fading channels,” Proc. Allerton Conf. on Comm., Control, and Comput., Monticello, Ill., October 2003, University of Illinois where the receiver employs successive decoders.
A finer outage formulation, in which an individual outage can be declared for each user, was developed in L. Li, N. Jindal et al., “Outage capacities and optimal power allocation for fading multiple-access channels,” IEEE Trans. Inform. Theory, vol. 51, no. 4, pp. 1326-47, April 2005 for the scenario where in addition to the receiver, each transmitting user has perfect CSI. Unfortunately, the absence of CSI at the user end considerably complicates the individual outage formulation. Essentially, the receiver should declare an individual outage for each user that it deems cannot be reliably decoded for the current channel state. Declaring a common outage for all users is very conservative since the receiver does not wish to make even a single error. On the other hand, an aggressive approach may yield a set of individual (per-user) outage probabilities that is not achievable (i.e., error probabilities arbitrarily close to these outage probabilities cannot be attained) and hence of little use. Obtaining a “good” set of achievable individual outage probabilities, where many if not all are smaller than the common outage probability, is difficult for the successive decoder due to the intractability of precisely modeling error propagation and is not known for the maximum likelihood (ML) decoder.
Successive group decoders (SGDs) were introduced in M. K. Varanasi, “Group detection for synchronous gaussian code-division multiple-access channels,” IEEE Trans. Inform. Theory, vol. 41, no. 4, pp. 1083-1096, July 1995, for the uncoded Gaussian CDMA channel, and are an extension of the conventional successive decoder in that at each decoding stage a subset of users can be jointly decoded instead of just one. The useful feature of such decoders is that they provide the system designer with a broad choice, spanning from the low-complexity successive decoder to the high-complexity ML decoder. Moreover, they are inherently better suited to a MAC (as opposed to the MIMO point-to-point system) since coding across transmitters (users) is not possible.
A SISO point-to-point channel is considered in S. A. Jafar et al., “Throughput maximization with multiple codes and partial outages,” in Proc. IEEE Global Telecommun. Conf., San Antonio, Tex., 2001 (hereinafter “Jafar et al.), where the transmitter employs multiple codes and the receiver uses the successive decoder. The successive decoder in Jafar et al. stops decoding at the first instance when an outage occurs, i.e., when the effective (scalar) channel cannot support the rate, and outages are declared for the current and remaining codes.
A joint decoder for a two-user symmetric MAC is proposed in S. Shamai et al., “A broadcast approach for a single-user slowly fading MIMO channel,” IEEE Trans. Inform. Theory, vol. 49, no. 10, pp. 2617-2635, October 2003, which works as follows. It first determines if both users can be decoded reliably via the ML decoder, if not it checks if any one of the users can be decoded reliably via either one of the two successive decoders (defined by decoding orders {1,2} and {2,1}, respectively) after treating the other user as a Gaussian interferer. Outage is declared for users deemed undecodable.